1. Field of the Invention
The present invention relates to a vector control method for a synchronous reluctance motor. More particularly, the invention relates to a vector control method using an estimator, instead of a salient pole position angle detector mounted on a rotor, in order to secure cosine and sine information of a rotor""s salient pole position angle necessary for a vector rotators for the vector control.
2. Description of the Related Art
To obtain superior drive control performance of a synchronous reluctance motor, the vector control method is conventionally employed as a well-known control method for controlling a stator current, which is essential for superior performance. The vector control method has a current control process which divides and controls the stator current contributing to the generation of a torque into a d-axis component and a q-axis component of rotational d-q coordinates composed of mutually orthogonal d and q axes which mutually cross at right angles.
Generally, d-q coordinates synchronized with the position of the main salient pole of the rotor with zero spatial phase difference are employed as rotational d-q coordinates for the vector control system. In other words, the use of synchronous d-q coordinates whose d-axis is oriented to direction of the main salient pole of the rotor and whose q-axis is orthogonal to the d-axis is very popular. Generally, the position angle of the main salient pole direction must be known in order to maintain the rotational d-q coordinates in a synchronized state free from the spatial phase difference with the main salient pole direction. Conventionally, in order to accurately ascertain the position angle, a salient position angle detector represented by an encoder mounted on the rotor.
FIG. 13 is a block diagram schematically showing a typical example of the vector control method using a salient pole position angle detector employed in a device which is in turn mounted on a standard synchronous reluctance motor which can disregard iron losses. In FIG. 13, 1 is a synchronous reluctance motor, 2 is a salient pole position angle detector, 3 is a power inverter, 4 is a current detector, 5a, 5b are a 3-2 phase converter and a 2-3 phase converter, 6a, 6b are vector rotators, 7 is a cosine and sine signal generator, 8 is a current controller, 9 is a command converter, 10 is a speed controller, and 11 is a speed detector. Components 4 to 9 in FIG. 13 configure a vector controller. For clarity and simplicity, a single solid bold line in FIG. 13 indicates a 2xc3x971 vector signal deeply related to the present invention. Block diagrams in the following are illustrated in the same manner.
In a conventional device such as in FIG. 13, the salient pole position angle detector 2 detects the main salient pole direction as an angle with respect to the center of a U-phase winding, and the cosine and sine signal generator 7 outputs its cosine and sine signals to the vector rotators 6a, 6b. Together, these comprise a means for determining a spatial phase of the rotational d-q coordinates. In the synchronous reluctance motor, the rotor speed is the rotation speed of the rotor""s salient pole. In other words, the rotor salient pole position angle and the rotor speed are in a relation of integration and differentiation, and it is known well by those killed in the art that speed information can be obtained from the salient pole position angle detector such as an encoder as well as the position angle information. The speed detector 11 is a one realizing such speed detecting means. The aforesaid five components 4, 5a, 5b, 6a, 6b, 7, 8 comprise a means for performing a current control process to divide the stator current into a d-axis component and a q-axis component on the rotational d-q coordinates, and to control the respective components to follow the current commands of the d-axis and the q-axis.
The 3-phase current detected by the current detector 4 is transformed by the 3-2 phase converter 5a into a 2-phase current on the stationary coordinates, which is, in turn, converted by the vector rotator 6a into 2-phase currents id, iq , on the rotational d-q coordinates and sent to the current controller 8. The current controller 8 generates voltage commands v*d, v*q on the rotational d-q coordinates and sends these to the vector rotator 6b so that the converted currents id, iq follow respective current commands i*d, i*q. The vector rotator 6b converts the 2-phase signals v*d, v*q into 2-phase voltage command on the stationary coordinates and sends this to the 2-3 phase converter 5b. The 2-3 phase converter 5b converts the 2-phase signal into a 3-phase voltage command and outputs it as a command to the power inverter 3. The power inverter 3 produces power corresponding to the command and applies it to the synchronous reluctance motor 1 to drive it. At that time, the current command is obtained by converting the torque command by the command converter 9. In this example of the speed control system, a torque command is obtained as output of the speed controller 10, to which the speed command and the detected speed are input. It is known well by those skilled in the art that when it is aimed to control the torque generation and not to configure the speed control system, the speed controller 10 and the speed detector 11 are not necessary. In such a case, the torque command can be directly applied from outside.
In order to realize the conventional vector control method for the synchronous reluctance motor, the salient pole position angle detector for detecting the salient pole position angle of the rotor is required, as described in the aforesaid typical example. However, fitting of the salient pole position angle detector such as an encoder to the rotor leads to the certain heretofore unavoidable problems, as described below.
A first problem is the deterioration in the reliability of the motor system. Although mechanically the synchronous reluctance motor is one of the strongest types of AC motor, as can be seen from the structure of the rotor, the salient pole position angle detector such as an encoder is mechanically much weaker than the motor body. Consequently, the placement of the salient pole position angle detector decreases extremely the overall mechanical reliability of the motor system. In addition to the deterioration in the mechanical reliability, the reliability decrease of the motor system due to the fitting of the salient pole position angle detector also occurs in an electrical aspect observed as contamination of the salient pole position angle detector signal with power supply noise, and also a thermal aspect observed as a temperature increase in the salient pole position angle detector due to heat from the rotor. Thus, the attachment of the salient pole position angle detector such as an encoder to the motor rotor has extremely decreased the reliability of the motor system.
A second problem is increase in motor size. The attachment of the salient pole position angle detector to the rotor increases the volume of the motor in its axial direction by at least several percent to as much as 50% or more according to the volume of the motor itself.
A third problem is the necessity to secure a source of power for operating the salient pole position angle detector, wiring of a signal line to receive a detection signal and a space for wiring. Naturally, to operate the salient pole position angle detector and to obtain information about the main salient pole position angle of the rotor from the detector, wiring therefor is necessary. The signal line is also generally required to have the same strength as the power line for driving the motor body in order to prevent degradation of the mechanical, electrical, and thermal reliability. As a result, a signal line having substantially the same size as the power line and also a space are generally necessary for a single motor.
A fourth problem is an increase in cost. In the production of a compact motor, the cost of the salient pole position angle detector might become higher than that of the motor body. Also, the cost of wiring for the salient pole position angle detector cannot be disregarded, especially for a compact motor. Maintenance costs also inevitably increase when reliability decreases. These various costs increase according to the number of motors used. Especially, the maintenance cost has a property of increasing exponentially in proportion to the quantity of motors.
The above problems result directly or indirectly from the salient pole position angle detector and can be remedied naturally if a so-called sensorless vector control method that does not require the salient pole position angle detector is established. Various types of a sensorless vector control methods have been developed for an induction motor and a permanent magnet synchronous motor among other A.C. motors though they have a different level of perfection, and they are used for the application depending on the perfection. Development of a sensorless vector control method for the synchronous reluctance motor is expected, but has not yet been reduced to practice.
The present invention was achieved under the aforesaid circumstances. The object of the invention is to provide a novel vector control method which does not require the salient pole position angle detector such as an encoder for a synchronous reluctance motor in order to solve the aforesaid problems related to the synchronous reluctance motor drive control. More particularly, it is the object of the present invention to provide a vector control method that can accurately and efficiently estimate cosine and sine signals as rotation signals for the vector rotators.
In order to achieve the above object, the present invention provides a vector control method for a synchronous reluctance motor, which has a current control process for controlling to divide a stator current contributing to generation of a torque into a d-axis component and a q-axis component of a current vector on a rotational d-q coordinates with mutually orthogonal d and q axes for vector rotators, wherein a stator linkage flux is caught as a stator magnetic flux vector, the stator magnetic flux vector is divided into an in-phase magnetic flux vector having the same direction as the current vector and a mirror-phase magnetic flux vector determined as a difference between the stator magnetic flux vector and the in-phase magnetic flux vector, and estimates of cosine and sine of an intermediate angle of the angles formed by the in-phase magnetic flux vector and the mirror-phase magnetic flux vector are used as a rotation signal of the vector rotators.
In another aspect, the present invention provides a vector control method for a synchronous reluctance motor as above, but wherein estimates of cosine and sine of a double angle of the intermediate angle are determined from the in-phase magnetic flux vector or its estimate value and the mirror-phase magnetic flux vector or its estimate value, and estimates of cosine and sine of the intermediate angle are determined from the determined estimates of cosine and sine of the double angle.
According to still another aspect, the present invention provides a vector control method for a synchronous reluctance motor as above, wherein determining the estimates of cosine and sine of the intermediate angle from the estimates of cosine and sine of the double angle is changed depending on an expected magnitude of the estimates of cosine and sine of the intermediate angle.
According to still another aspect, the present invention is a vector control method for a synchronous reluctance motor as above, wherein the in-phase magnetic flux vector or a vector having the same direction as its estimate value and the mirror-phase magnetic flux vector or a vector having the same direction as its estimate value, both of which are normalized so as to have the same norm, are produced, and respective estimates of cosine and sine of the intermediate angle are determined in proportion to a first component and a second component of a synthesis vector obtained by vector adding up the above produced two vectors having the same norm.
According to still another aspect, the present invention is a vector control method for a synchronous reluctance motor as above, wherein the in-phase magnetic flux vector or a vector having the same direction as its estimate value and the mirror-phase magnetic flux vector or a vector having the same direction as its estimate value, both of which having the same norm are produced, and respective estimates of cosine and sine of the intermediate angle are determined in skewed proportion to a synthesis vector obtained by vector subtraction of the above produced two vectors having the same norm.
The operation of the present invention will next be described. For the clear understanding of the invention, the operation will be described by using with reference to mathematical models in which iron loss is disregarded. Where the rotor of the synchronous reluctance motor is captured on a general d-q coordinates rotating at an instantaneous angular velocity xcfx89, it can be illustrated as shown in FIG. 1. In FIG. 1, the d-q coordinates are not necessarily in synchronization with the direction of a main salient pole of the rotor. Therefore, the d-q coordinates are assumed to be general. A circuit characteristic of the synchronous reluctance motor in the above state can be expressed by the following circuit equations in (1) and (2).
xcexd1=R1i1+[sI+xcfx89J]xcfx861xe2x80x83xe2x80x83(1)
xcfx861=[LaI+LbQ(xcex8)]i1xe2x80x83xe2x80x83(2)
A characteristic of the torque generation can be expressed by the following equation (3).
xe2x80x83xcfx84=NpLbi1TJQ(xcex8)i1xe2x80x83xe2x80x83(3)
In the equations (1) to (3), xcexd1, i1 and xcfx861 are 2xc3x971 vectors respectively denoting a stator voltage, a stator current and a stator linkage magnetic flux (stator magnetic flux), and R1 denotes a copper-loss resistance of the stator, Np denotes the number of pole pairs, s denotes a differential operator d/dt. And, J denotes a skew symmetric matrix defined by the following equation (4).                     J        =                  [                                                    0                                                              -                  1                                                                                    1                                            0                                              ]                                    (        4        )            
In the equations (2) and (3), Q(xcex8) denotes a mirror matrix defined by the following equation (5).                               Q          ⁡                      (            θ            )                          =                  [                                                                      cos                  ⁢                                      xe2x80x83                                    ⁢                  2                  ⁢                  θ                                                                              sin                  ⁢                                      xe2x80x83                                    ⁢                  2                  ⁢                  θ                                                                                                      sin                  ⁢                                      xe2x80x83                                    ⁢                  2                  ⁢                  θ                                                                                                  -                    cos                                    ⁢                                      xe2x80x83                                    ⁢                  2                  ⁢                                      xe2x80x83                                    ⁢                  θ                                                              ]                                    (        5        )            
As shown in FIG. 1, xcex8 of the mirror matrix denotes an instant position angle of the main salient pole of the rotor rotating at an electrical angular velocity xcfx892n with respect to the d-axis of the general d-q coordinates.
To perform vector control, the rotational d-q coordinates are selected so that xcex8 becomes zero, or, in other words, so that the rotational d-q coordinates synchronizes with the main salient pole position with zero phase-difference. On the synchronous d-q coordinates, the torque generation formula of the equation (3) can be reproduced in a simple form as indicated by the equation (6).
xcfx84=2NpLbidiqxe2x80x83xe2x80x83(6)
Specifically, the generated torque is proportional to the respective d, q components id, iq of the stator current vector. Based on the above relation, the torque generation can be controlled through control of the d, q components of the stator current by means of appropriate current control systems.
However, for the equation (6) for the synchronous reluctance to be valid, it is necessary to construct the synchronous d-q coordinates in synchronization with the main salient pole position angle of the rotor without a phase difference. Therefore, conventionally, the salient pole position angle detector such as an encoder, is conventionally mounted on the rotor in order to detect the position angle on the stationary coordinates, and the resulting cosine and sine values were used for the vector rotators described by the 2xc3x972 matrix of the following equation (7), which perform coordinate transformation between the stationary coordinates and the synchronous coordinates.                               R          ⁡                      (            θ            )                          =                  [                                                                      cos                  ⁢                                      xe2x80x83                                    ⁢                  θ                                                                                                  -                    sin                                    ⁢                                      xe2x80x83                                    ⁢                  θ                                                                                                      sin                  ⁢                                      xe2x80x83                                    ⁢                  θ                                                                              cos                  ⁢                                      xe2x80x83                                    ⁢                  θ                                                              ]                                    (        7        )            
According to the present invention, the stator magnetic flux vector indicated by the equation (2) is divided into an in-phase magnetic flux vector xcfx86a having the same direction as the current vector, and a mirror-phase magnetic flux vector xcfx86b determined as a difference between the stator flux vector and the in-phase flux vector. An intermediate angle among the angles formed by both of the flux vectors is determined as an estimate value of the main salient pole position angle xcex8 of the rotor. In the present invention, the in-phase flux vector xcfx86a and the mirror-phase flux vector xcfx86b are determined as indicated by the following equations (8), (9).
xcfx86a=Lai1xe2x80x83xe2x80x83(8)
xcfx86b=xcfx861xe2x88x92xcfx86a=LbQ(xcex8)i1xe2x80x83xe2x80x83(9)
Then, it will be described that the intermediate angle among the angles formed by both of the flux vectors can be used as an estimate value of the main salient pole position angle xcex8 of the rotor. In order to simplify the description in the following, a unit vector that has the same angle as the main salient pole position angle is defined as                               u          ⁡                      (            θ            )                          =                              [                                                                                cos                    ⁢                                          xe2x80x83                                        ⁢                    θ                                                                                                                    sin                    ⁢                                          xe2x80x83                                        ⁢                    θ                                                                        ]                    .                                    (        10        )            
The stator current i1 can be expressed in the general d-q coordinates as
i1=∥i1∥u(xcex8a)=∥i1∥R(xcex8axe2x88x92xcex8)u(xcex8)xe2x80x83xe2x80x83(11)
where xcex8a is the position angle of the current. The in-phase flux is synchronized with the stator current with zero phase-difference as shown in the equation (8) and can be evaluated as indicated by the following equation (12).
xcfx86a=La∥i1∥R(xcex8axe2x88x92xcex8)u(xcex8)xe2x80x83xe2x80x83(12)
Meanwhile, the mirror-phase flux can be reevaluated as indicated by the equation (13) in view of the equations (9) and (11).                                                                         φ                b                            =                              xe2x80x83                            ⁢                                                L                  b                                ⁢                                  "LeftDoubleBracketingBar"                                      i                    1                                    "RightDoubleBracketingBar"                                ⁢                                  Q                  ⁡                                      (                    θ                    )                                                  ⁢                                  R                  ⁡                                      (                                                                  θ                        a                                            -                      θ                                        )                                                  ⁢                                  u                  ⁡                                      (                    θ                    )                                                                                                                          =                              xe2x80x83                            ⁢                                                L                  b                                ⁢                                  "LeftDoubleBracketingBar"                                      i                    1                                    "RightDoubleBracketingBar"                                ⁢                                  R                  ⁡                                      (                                          -                                              (                                                                              θ                            a                                                    -                          θ                                                )                                                              )                                                  ⁢                                  Q                  ⁡                                      (                    θ                    )                                                  ⁢                                  u                  ⁡                                      (                    θ                    )                                                                                                                          =                              xe2x80x83                            ⁢                                                L                  b                                ⁢                                  "LeftDoubleBracketingBar"                                      i                    1                                    "RightDoubleBracketingBar"                                ⁢                                  R                  ⁡                                      (                                          -                                              (                                                                              θ                            a                                                    -                          θ                                                )                                                              )                                                  ⁢                                  u                  ⁡                                      (                    θ                    )                                                                                                          (        13        )            
The equations (12) and (13) describe that the in-phase vector and the mirror-phase vector are mutually in a state of opposite phases with respect to the main salient pole position angle of the rotor. In other words, they indicate that the intermediate angle among the angles formed by both of the flux vectors can be handled as an estimate value of the main salient pole position angle xcex8 of the rotor. Cosine and sine values of the estimate value of the main salient pole position angle xcex8 naturally become estimates of cosine and sine of the main salient pole position angle xcex8. The estimates of cosine and sine obtained as described above are used for the vector rotators necessary for the synchronous d-q coordinates in the present invention. In order to assist understanding of the present invention, the relationships among the vectors of the stator current, the stator flux, the in-phase flux and the mirror-phase flux on the general d-q coordinates described by the equations (8) to (13) are illustrated as a vector diagram in FIG. 2.
It is then apparent from the above description that according to the present invention, there is obtained an operation that the estimates of cosine and sine of the rotor main salient pole position angle necessary for the vector rotators in order for the vector control without using the salient pole position angle detector to be mounted on the rotor.
Then, the operation of a further aspect of the present invention will be described. It was described with reference to the equations (8) to (13) that the in-phase flux vector and the mirror-phase flux vector were in a state of opposite phases from each other with respect to the main salient pole position angle of the rotor. Such a relationship can be indicated by the following equation (14) using the main salient pole position angle xcex8 and the respective position angles xcex8a, xcex8b of the in-phase and mirror-phase flux vectors.
xe2x80x832xcex8=xcex8a+xcex8bxe2x80x83xe2x80x83(14)
The signal necessary for the vector rotators for the vector control is not the position angle itself of the rotor main salient pole but its cosine and sine values. In other words, the following relation is also important for application.                               u          ⁡                      (                          2              ⁢                              xe2x80x83                            ⁢              θ                        )                          =                              [                                                                                cos                    ⁢                                          xe2x80x83                                        ⁢                    2                    ⁢                    θ                                                                                                                    sin                    ⁢                                          xe2x80x83                                        ⁢                    2                    ⁢                                          xe2x80x83                                        ⁢                    θ                                                                        ]                    =                      [                                                                                                      cos                      ⁢                                              xe2x80x83                                            ⁢                                              θ                        a                                            ⁢                      cos                      ⁢                                              xe2x80x83                                            ⁢                                              θ                        b                                                              -                                          sin                      ⁢                                              xe2x80x83                                            ⁢                                              θ                        a                                            ⁢                      sin                      ⁢                                              xe2x80x83                                            ⁢                                              θ                        b                                                                                                                                                                                    sin                      ⁢                                              xe2x80x83                                            ⁢                                              θ                        a                                            ⁢                      cos                      ⁢                                              xe2x80x83                                            ⁢                                              θ                        b                                                              +                                          cos                      ⁢                                              xe2x80x83                                            ⁢                                              θ                        a                                            ⁢                      sin                      ⁢                                              xe2x80x83                                            ⁢                                              θ                        b                                                                                                                  ]                                              (        15        )            
The right side of the equation (15) can be calculated directly from the in-phase and mirror-phase fluxvectors. For example, it may be simply calculated by the following equation (16).                               u          ⁡                      (                          2              ⁢                              xe2x80x83                            ⁢              θ                        )                          =                                            [                                                φ                  a                                ⁢                J                ⁢                                  xe2x80x83                                ⁢                                  φ                  a                                            ]                        ⁢                          φ              b                                                          "LeftDoubleBracketingBar"                              φ                a                            "RightDoubleBracketingBar"                        ⁢                          "LeftDoubleBracketingBar"                              φ                b                            "RightDoubleBracketingBar"                                                          (        16        )            
The following general trigonometric function for the double angle is well known.                               [                                                                      cos                  ⁢                                      xe2x80x83                                    ⁢                  2                  ⁢                  θ                                                                                                      sin                  ⁢                                      xe2x80x83                                    ⁢                  2                  ⁢                                      xe2x80x83                                    ⁢                  θ                                                              ]                =                              [                                                                                                      2                      ⁢                                              xe2x80x83                                            ⁢                                              cos                        2                                            ⁢                      θ                                        -                    1                                                                                                                    2                    ⁢                    sin                    ⁢                                          xe2x80x83                                        ⁢                    θcos                    ⁢                                          xe2x80x83                                        ⁢                    θ                                                                        ]                    =                      [                                                                                1                    -                                          2                      ⁢                                              sin                        2                                            ⁢                      θ                                                                                                                                        2                    ⁢                                          xe2x80x83                                        ⁢                    sin                    ⁢                                          xe2x80x83                                        ⁢                    θ                    ⁢                                          xe2x80x83                                        ⁢                    cos                    ⁢                                          xe2x80x83                                        ⁢                    θ                                                                        ]                                              (        17        )            
It can be seen from the above that, when the cosine and sine values of the double angle of the main salient pole position are known, the cosine and sine values of the main salient pole position can be determined from the relationship of the equation (17).
According to another aspect, the present invention is a vector control method as above, wherein the estimates of cosine and sine of the double angle of the intermediate angle are determined from the in-phase flux vector or its estimate value and the mirror-phase flux vector or its estimate value, and the estimates of cosine and sine of the intermediate angle are determined from the determined estimates of cosine and sine of the double angle. It is apparent from the above description with reference to the equations (16) and (17) that the present invention can provide the direct calculation of the estimates of cosine and sine necessary for the vector rotators from the in-phase and mirror-phase flux vectors themselves without calculating the position angles of the in-phase flux vector and the mirror-phase flux vector. The calculation of the position angle from the vectors requires an inverse operation of a trigonometric function that is a kind of nonlinear functions. It is known that the inverse operation might cause a great error or need a large amount of computation depending on the position angle. In this aspect of the present invention, however, such an inverse operation is not necessary, and estimates of cosine and sine of the position angle can be determined with relatively high accuracy by a relatively light calculation. In other words, according to this aspect of the present invention, the operation described earlier can be obtained with relatively high accuracy by a relatively light calculation.
The operation of yet another aspect of the present invention will be described. When the relationship in the first row of the equation (17) is used to calculate the estimates of cosine and sine of the main salient pole position angle from the estimates of cosine and sine of the double angle of the rotor main salient pole position, a square root operation is required. When the relation of the second row of the equation (17) is used, division operation is required, but no square root operation is necessary. Generally, the amount of computation required for performing division is small compared with that for solving a square root, so that it is desirable to use the second row as much as possible. However, because in division the error tends to be large when the absolute value of denominator is extremely small, from a practical point of view it is desirable to avoid such instances. It is apparent from the above description that when the cosine value has a large absolute value, for example, it is preferable to have the determining method indicated by the following equation (18).                                           cos            ⁢                          xe2x80x83                        ⁢            θ                    =                      ±                                                            1                  +                                      cos                    ⁢                                          xe2x80x83                                        ⁢                    2                    ⁢                                          xe2x80x83                                        ⁢                    θ                                                  2                                                    ,                              sin            ⁢                          xe2x80x83                        ⁢            θ                    =                                    sin              ⁢                              xe2x80x83                            ⁢              2              ⁢              θ                                      2              ⁢              cos              ⁢                              xe2x80x83                            ⁢              θ                                                          (        18        )            
Meanwhile, when the sine value has a large absolute value, the determining method indicated by the following equation (19) is preferable.                                           sin            ⁢                          xe2x80x83                        ⁢            θ                    =                      ±                                                            1                  -                                      cos                    ⁢                                          xe2x80x83                                        ⁢                    2                    ⁢                                          xe2x80x83                                        ⁢                    θ                                                  2                                                    ,                              cos            ⁢                          xe2x80x83                        ⁢            θ                    =                                    sin              ⁢                              xe2x80x83                            ⁢              2              ⁢              θ                                      2              ⁢              sin              ⁢                              xe2x80x83                            ⁢              θ                                                          (        19        )            
In a further aspect of the vector control method as described above, the method of determining the estimates of cosine and sine of the intermediate angle from the estimates of cosine and sine of the double angle is varied according to a predicted magnitude of the estimates of cosine and sine of the intermediate angle. As a result, it is apparent from the above description, referring to the equations (18) and (19), that there is obtained an operation that the estimates of cosine and sine can be determined as the rotation signal for the vector rotators in the state maintaining the highest computation accuracy, as well as in the state that the amount of computation is reduced rationally. In addition, according to this aspect of the present invention, the operation described above can be obtained with a high accuracy and a rationalized amount of calculation.
Next, the operation of yet another aspect of the present invention will be described. In this aspect of the present invention, in a vector control method described above, the in-phase flux vector or a vector having the same direction as its estimate value and the mirror-phase flux vector or a vector having the same direction as its estimate value, both of which having the same norm are produced, and respective estimates of cosine and sine of the intermediate angle are determined in proportion to a first component and a second component of a synthesis vector obtained by vector adding up the two vectors having the same norm.
FIG. 3 illustrates the above vector synthesis on a general d-q coordinates. In the drawing, the direction of the main salient pole of the rotor is indicated by a unit vector u(xcex8), and two vectors with the norm made the same are indicated by K2i1 and K2Q(xcex8)i1. The synthesis vector obtained by addition of such vectors is indicated by xcex6. It can be readily seen from FIG. 3 that the synthesis vector has the same direction as the main salient pole of the rotor. It is also possible to describe rigorously by using equations as given below that the synthesis vector by addition has the same direction as the unit vector indicating the main salient pole position.                                                                       =                              xe2x80x83                            ⁢                                                                    K                    2                                    ⁡                                      [                                                                                            φ                          a                                                                          L                          a                                                                    +                                                                        φ                          b                                                                          L                          b                                                                                      ]                                                  =                                                      K                    2                                    ⁡                                      [                                                                  i                        1                                            +                                                                        Q                          ⁡                                                      (                            θ                            )                                                                          ⁢                                                  i                          1                                                                                      ]                                                                                                                          =                              xe2x80x83                            ⁢                                                K                  2                                ⁢                                                                            u                      T                                        ⁡                                          (                      θ                      )                                                        ⁡                                      [                                                                  i                        1                                            +                                                                        Q                          ⁡                                                      (                            θ                            )                                                                          ⁢                                                  i                          1                                                                                      ]                                                  ⁢                                  u                  ⁡                                      (                    θ                    )                                                                                                                          =                              xe2x80x83                            ⁢                              2                ⁢                                                      K                    2                                    ⁡                                      (                                                                  i                        1                        T                                            ⁢                                              u                        ⁡                                                  (                          θ                          )                                                                                      )                                                  ⁢                                  u                  ⁡                                      (                    θ                    )                                                                                                          (        20        )            
The equation (20) proves that the additive synthesis vector becomes scalar multiple of the unit vector indicating the main salient pole position and that the description referring to FIG. 3 is valid.
It can be seen from the equation (20) that the cosine and sine values of the main salient pole position angle of the rotor can be estimated from the following relation.                                                                         u                ⁡                                  (                  θ                  )                                            =                              xe2x80x83                            ⁢                                                                2                  ⁢                                                            K                      2                                        ⁡                                          (                                                                        i                          1                          T                                                ⁢                                                  u                          ⁡                                                      (                            θ                            )                                                                                              )                                                                                                                                                              =                                  xe2x80x83                                ⁢                                                      sgn                    ⁡                                          (                                                                        K                          2                                                ⁢                                                  i                          1                          T                                                ⁢                                                  u                          ⁡                                                      (                            θ                            )                                                                                              )                                                        ⁢                                                                                "LeftDoubleBracketingBar"                                            "RightDoubleBracketingBar"                                                                                  ;                                                                    i                    1                    T                                    ⁢                                      u                    ⁡                                          (                      θ                      )                                                                      ≠                0                                                                        (        21        )            
Specifically, the estimates of cosine and sine of the intermediate angle can be determined in proportion to the first and second components of the synthesis vector by addition as described in this aspect of the present invention.
According to the present aspect, it is apparent from the above description referring to the equation (21) that there is obtained an operation that the estimates of cosine and sine of the intermediate angle and further the rotation signal necessary for the vector rotators can be determined by very simple calculation excepting an area where the absolute value of the inner product (i1Tu(xcex8)) of the stator current and the unit vector becomes small. As a result, according to the present aspect, the operation described can be achieved by very simple calculation. A method of avoiding the absolute value of the inner product of the stator current and the unit vector from becoming too small will be described in detail below with reference to an embodiment related to the present aspect.
The operation of a further aspect of the present invention will now be described. The present invention according to this aspect is a vector control method described above, wherein the in-phase flux vector or a vector having the same direction as its estimate value and the mirror-phase flux vector or a vector having the same direction as its estimate value, both of which having the same norm are produced, and respective estimates of cosine and sine of the intermediate angle are determined in skewed proportion to a synthesis vector obtained by vector subtraction of the above produced two vectors having the same norm.
FIG. 4 shows an appearance of the above vector synthesis on a general d-q coordinates. In the drawing, the direction of the main salient pole of the rotor is indicated by a unit vector u(xcex8), and two vectors having the norm made the same are indicated by K2i1 and K2Q(xcex8)i1. The synthesis vector obtained by subtraction of such vectors is indicated by xcex6. It is readily apparent from the same drawing that the direction of the synthesis vector becomes perpendicular to that of the rotor""s main salient pole. It is also possible to precisely describe this as follows with reference to a mathematical equation.                                                                       =                              xe2x80x83                            ⁢                                                                    K                    2                                    ⁡                                      [                                                                                            φ                          a                                                                          L                          a                                                                    -                                                                        φ                          b                                                                          L                          b                                                                                      ]                                                  =                                                      K                    2                                    ⁡                                      [                                                                  i                        1                                            -                                                                        Q                          ⁡                                                      (                            θ                            )                                                                          ⁢                                                  i                          1                                                                                      ]                                                                                                                          =                              xe2x80x83                            ⁢                                                K                  2                                ⁢                                                      u                    T                                    ⁡                                      (                    θ                    )                                                  ⁢                                                      J                    T                                    ⁡                                      [                                                                  i                        1                                            -                                                                        Q                          ⁡                                                      (                            θ                            )                                                                          ⁢                                                  i                          1                                                                                      ]                                                  ⁢                                  Ju                  ⁡                                      (                    θ                    )                                                                                                                          =                              xe2x80x83                            ⁢                              2                ⁢                                                      K                    2                                    ⁡                                      (                                                                  i                        1                        T                                            ⁢                                              Ju                        ⁡                                                  (                          θ                          )                                                                                      )                                                  ⁢                                  Ju                  ⁡                                      (                    θ                    )                                                                                                          (        22        )            
The equation (22) is used to ascertain that the direction of the subtraction synthesis vector is perpendicular to the unit vector indicating the main salient pole position and its size becomes scalar multiple, and also to prove the validity of the description with reference to FIG. 4.
It can be understood from the equation (22) that the cosine and sine values of the main salient pole position angle of the rotor can be estimated from the following relation.                                                                         u                ⁡                                  (                  θ                  )                                            =                              xe2x80x83                            ⁢                                                                    -                    J                                    ⁢                                      xe2x80x83                                    ⁢                                                                    2                  ⁢                                                            K                      2                                        ⁡                                          (                                                                        i                          1                          T                                                ⁢                                                  Ju                          ⁡                                                      (                            θ                            )                                                                                              )                                                                                                                                                              =                                  xe2x80x83                                ⁢                                                      -                                          sgn                      ⁡                                              (                                                                              K                            2                                                    ⁢                                                      i                            1                            T                                                    ⁢                                                      Ju                            ⁡                                                          (                              θ                              )                                                                                                      )                                                                              ⁢                                                            J                      ⁢                                              xe2x80x83                                            ⁢                                                                                    "LeftDoubleBracketingBar"                                            "RightDoubleBracketingBar"                                                                                  ;                                                                    i                    1                    T                                    ⁢                                      Ju                    ⁡                                          (                      θ                      )                                                                      ≠                0                                                                        (        23        )            
Specifically, as specified in the present invention, the estimates of cosine and sine of the intermediate angle can be determined in skewed proportion to the subtraction synthesis vector xcex6. It should be noted that the skewed proportion is expressed in terms of the skew symmetric matrix J acting on the subtraction synthesis vector xcex6 in (23), and that the skewed proportion, rather than a simple proportion, is required for the estimates because the synthesis vector xcex6 is perpendicular with respect to the main salient pole direction.
According to this aspect of the invention, it is readily apparent from the above description referring to the equation (23) that the estimates of cosine and sine of the intermediate angle, and further the rotation signal necessary for the vector rotators can be determined by very simple calculation excepting an area where the absolute value of skewed inner product (i1TJu(xcex8)) by the stator current and the unit vector becomes small. As a result, according to the present aspect, the operation described in the first aspect can be achieved through a relatively very simple calculation. A method of avoiding the absolute value of the skewed inner product by the stator current and the unit vector from becoming small will be described below in detail.